A one-dimensional Lagrangian code is used to study a simple example of the development of the inverse skin effect in a Z-pinch. The pinch expands although plasma at the surface does not detach itself. The code is then used to model the falling current phase of an experimental Z-pinch at Imperial College. The maximum rate of cooling of the pinch is deduced by comparing the simulated and the observed dynamical behaviour. Using this result the compressional pinch is shown to be anomalously stable.